Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.util.Scanner;

public class Main
{
    public static void main(String[] args) throws IOException
    {
        int i, j, m, n, vmin, ans, l, c;
        boolean ok;
        int[][] g;
        int[] lin, col;
        Scanner in = new Scanner(System.in);

        m = in.nextInt();
        n = in.nextInt();
        lin = new int[m];
        col = new int[n];
        g = new int[m][n];

        vmin = 510; l = -1; c = -1;
        for(i = 0; i < m; ++i)
            for(j = 0; j < n; ++j)
            {
                g[i][j] = in.nextInt();
                if(g[i][j] < vmin) { vmin = g[i][j]; l = i; c = j; }
            }

        ans = Math.min(m, n) * vmin;
        if(m < n)
        {
            for(i = 0; i < m; ++i) lin[i] += vmin;
        }
        else
        {
            for(j = 0; j < n; ++j) col[j] += vmin;
        }

        for(i = 0; i < m; ++i)
            for(j = 0; j < n; ++j)
                g[i][j] -= vmin;

        for(i = 0; i < m; ++i) { lin[i] += g[i][c]; ans += g[i][c]; }
        for(j = 0; j < n; ++j) { col[j] += g[l][j]; ans += g[l][j]; }

        ok = true;
        for(i = 0; i < m; ++i)
            for(j = 0; j < n; ++j)
                if(lin[i] + col[j] != g[i][j] + vmin)
                    ok = false;

        if(ok)
        {
            System.out.println(ans);
            for(i = 0; i < m; ++i)
                for(j = 0; j < lin[i]; ++j)
                    System.out.println("row " + (i + 1));

            for(j = 0; j < n; ++j)
                for(i = 0; i < col[j]; ++i)
                    System.out.println("col " + (j + 1));
        }
        else
        {
            System.out.println(-1);
        }
    }
}